The Council members said in a statement that they welcomed the announcement of the "conditional ceasefire" with the Taliban from the start of the Eid al-Adha holiday, which began in the evening of Aug. 21 and ended on Aug. 25.
Traditionally, the festival lasts for four days but public holidays vary around the world, with Arab countries observing a nine-day public holiday.
"The members of the Security Council reiterated the importance of an inclusive Afghan-led and -owned peace process for the long-term prosperity and stability of Afghanistan, and expressed their full support for the Afghan government`s efforts to that end," according to the statement, as quoted by Xinhua.
In the wake of a string of deadly attacks, the Afghan president on Aug. 19 offered a monthlong ceasefire with the Taliban, if the militant group agrees to honor it.
The Taliban has yet to respond to Ashraf Ghani`s overture but said it would release hundreds of prisoners to celebrate the Islamic holiday of Eid al-Adha, also known as the Festival of Sacrifice.
Afghan government in June extended its unilateral ceasefire with the Taliban following an initial truce observed by both sides over the Eid al-Fitr holiday, an important religious holiday celebrated by Muslims worldwide that marks the end of Ramadan, the Islamic holy month of fasting.